What is the equation of a parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2)? x= –y216+6y16–4116 y= –x216+6x16–4116 y=x216–6x16+4116 x=y216–6y16+4116
Answers
Answer:
y=x216–6x16+4116
Step-by-step explanation:
plato :)
The equation of the parabola is in option (C) if the parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2) option (C) is correct.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
It is given that:
The equation of a parabola that has a vertical axis, passes through the point (–1, 3)
The vertex of the parabola is at (3, 2)
As we know, in the standard form of the parabola (h, k) represents the vertex of the parabola.
h = 3
k = 2
Plug the above point in the equation:
[tex]\rm y\ =\ \dfrac{x^{2}}{16}-\dfrac{6x}{16}+\dfrac{41}{16}[/tex]
x = 3
y = 2
[tex]\rm 2\ =\ \dfrac{3^{2}}{16}-\dfrac{6(3)}{16}+\dfrac{41}{16}[/tex]
= 9/16 - 18/16 + 41/16
= (9-18+41)/16
= 32/16
2 = 2 ( true)
The equation of the parabola is:
[tex]\rm y\ =\ \dfrac{x^{2}}{16}-\dfrac{6x}{16}+\dfrac{41}{16}[/tex]
Thus, the equation of the parabola is in option (C) if the parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2) option (C) is correct.
Learn more about the parabola here:
brainly.com/question/8708520
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Related Questions
Please help
Given: F is the midpoint of AE and AB ll DE
Prove: △BFA = △DFE
Statements and Reasons
Answers
Answer:
See Below.
Step-by-step explanation:
We can write a two-column proof.
Statements: Reasons:
[tex]\displaystyle 1)\, F\text{ is the midpoint of } AE[/tex] Given
[tex]\displaystyle 2) \, \overline{FA} \cong \overline{FE}[/tex] Definition of Midpoint
[tex]\displaystyle 3) \, AB\parallel DE[/tex] Given
[tex]\displaystyle 4)\, \angle B \cong \angle D[/tex] Alt. Int. Angles Are Congruent
[tex]\displaystyle 5)\, \angle A \cong E[/tex] Alt. Int. Angles Are Congruent
[tex]\displaystyle 6) \, \Delta BFA \cong \Delta DFE[/tex] AAS Congruence
If the length of a leg of a right triangle is 25 and the length of the hypotenuse is 35, what's the length of the other leg, to the nearest tenth?
Answers
Answer:
24.5
Step-by-step explanation:
using Pythagorean theorem
[tex]a^{2} +b^{2} =c^{2} \\[/tex]
Since we know the hypotenuse, we can change up the theorem into [tex]c^{2} -b^{2} =a^{2}[/tex]
[tex]35^{2} -25^{2} =a^{2}[/tex]
1225-625=[tex]a^{2}[/tex]
[tex]\sqrt{a^{2} } =24.5[/tex]
Determine whether the point (4,2) is in the solution set of the system of inequalities below. 4x + y < 2 y > –2
Answers
Answer:
False
Step-by-step explanation:
4x + y < 2
y > –2
Substitute the point into the inequalities and see if they are true
4(4) + 2 < 2
16+2 < 2
18 <2 False
2 > –2 True
Since one is false the point is not a solution
a rice cooker was sold for $60 after a discount of 60% waht was the usual price of the rice cooker
Answers
Discounted price = $60
Discount = 60%
Let the usual price be x.
So, x - (60% of x) = $60
=> x - [(60/100) × x] = $60
=> x - (60x/100) = $60
=> x - (3x/5) = $60
=> (5x/5) - (3x/5) = $60
=> 2x/5 = $60
=> 2x = $60 × 5
=> 2x = $300
=> x = $300/2
=> x = $150
So, the usual price is $150.
Leah is looking to take out a 30-year mortgage from a bank offering a monthly interest rate of 0.325% Using the formula below, determine the maximum amount Leah can borrow, to the nearest dollar, if the highest monthly payment she can afford is $900.
M=Pr/(1-(1+r)^-n)
M= the monthly payment
P= the amount owed
r= the interest rate per month
n= the number of payments
Answers
Answer:
[tex]P=\$276646.153[/tex]
Step-by-step explanation:
Time [tex]T=30years[/tex]
Rate [tex]r=0.325\%[/tex]
Payment per month [tex]P=\$ 900[/tex]
Generally the equation for Principle is mathematically given by
[tex]M=\frac{P r}{1-(1+r)^{-n}}[/tex]
[tex]900=\frac{P \frac{0.325}{100}}{1-(1+( \frac{0.325}{100}))^{- 30*12}}[/tex]
[tex]P=\frac{900*100*0.99}{0.325}[/tex]
[tex]P=\$276646.153[/tex]
The mortgage on your new house is $180,000. Your monthly mortgage payment is $839 for 30 years. How much interest will be paid if the house is kept for the full 30 years?
Answers
9514 1404 393
Answer:
$122,040
Step-by-step explanation:
The interest is the difference between the mortgage value and the total amount paid.
($839/mo)×(12 mo/yr)×(30 yr) -180,000 = $302,400 -180,000 = $122,040
$122,040 will be paid in interest.
Which of the following is graphed below?
Answers
Dutchess County, New York, has been experiencing a mean of 35.4 motor vehicle deaths each year. If D = the number of vehicle deaths in Dutchess County in a year, what is the distribution for D (Binomial or Poisson) Explain.
Answers
Answer:
Poisson, as we have the mean number and not a proportion.
Step-by-step explanation:
We have the mean number of vehicle deaths per year, thus, since it is a mean and not a proportion, we use the Poisson distribution.
If we were working with the proportion of accidents that end in death for example, or any other proportion, it would be a binomial random variable.
The sum of two integers is 90 and their difference is 30. Find the larger number
Answers
Answer:
60 is the larger number
Step-by-step explanation:
Let the two numbers be a and y
x+y = 90
x-y = 30
Add the two equations together
x+y = 90
x-y = 30
-----------------
2x = 120
Divide by 2
2x/2 =120/2
x = 60
x+y =90
60+y = 90
y = 90-60
y = 30
The numbers are 60 and 30
The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,450. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 570 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last.
How many pages should the manufacturer advertise for each cartridge if it wants to be correct 90 percent of the time? (Round z value to 2 decimal places. Round your answer to the nearest whole number.)
Answers
Answer:
The manufacturer should advertise 11720 pages.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 12450, standard deviation of 570:
This means that [tex]\mu = 12450, \sigma = 570[/tex]
How many pages should the manufacturer advertise for each cartridge if it wants to be correct 90 percent of the time?
They should advertise the 10th percentile, which is X when Z has a p-value of 0.1, so X when Z = -1.28. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 12450}{570}[/tex]
[tex]X - 12450 = -1.28*570[/tex]
[tex]X = 11720[/tex]
The manufacturer should advertise 11720 pages.
Find the exact value of the logarithm without using a calculator.
Answers
Answer:
1/11
Step-by-step explanation:
We are asked to find the natural log of
[tex] \sqrt[11]{e} [/tex]
Convert to fractional exponent
[tex] ln(e {}^{ \frac{1}{11} } ) [/tex]
Apply Log of Power rule
[tex] \frac{1}{11} ln(e) [/tex]
Natural log of e is 1 so
[tex] \frac{1}{11} \times 1 = \frac{1}{11} [/tex]
Answer:
[tex]\frac{1}{11}[/tex]
Step-by-step explanation:
First, remember that the ln function is just a log function with a base of e. Here's how it looks
[tex]ln(x) =log_{e}(x)[/tex]
[tex]ln(\sqrt[11]{e} ) = log_{e}(\sqrt[11]{e} )[/tex]
We can take this one step further if we realize that we can rewrite the square root as a simple power to a fraction!
[tex]log_{e}(e^{\frac{1}{11} } )[/tex]
Solving the equation above is really simple. All that function is really saying is can we raise e to some number, where the result would be e^(1/11)? In other words find x.
[tex]e^{x} = e^{\frac{1}{11} }[/tex]
Well x has to be 1/11 in that case. And that ends up being our final answer.
[tex]log_{e}(e^{\frac{1}{11} } ) = \frac{1}{11}[/tex]
Find all solutions to the following system of equations.
x = 1.5x(1 − x) − 0.6xy
y = y + 2xy − 0.5y
(x, y) = (
Incorrect: Your answer is incorrect.
(smallest x-value)
(x, y) =
Incorrect: Your answer is incorrect.
(x, y) =
Incorrect: Your answer is incorrect.
(largest x-value)
Answers
9514 1404 393
Answer:
(x, y) = (0, 0), (1/3, 0), (1/4, 5/24)
Step-by-step explanation:
It is often helpful to write equations in general form. That way, factoring and use of the zero product rule can find solutions.
x = 1.5x(1 -x) -0.6xy . . . . given
1.5x -1.5x² -0.6xy -x = 0 . . . . . subtract x
0.5x -1.5x² -0.6xy = 0 . . . . . . . collect terms
0.1x(5 -15x -6y) = 0 . . . . . . . . factor; [eq1]
__
y = y +2xy -0.5y . . . . . . given
y +2xy -0.5y -y = 0 . . . . . subtract y
-0.5y +2xy = 0 . . . . . . . . . . collect terms
-0.5y(1 -4x) = 0 . . . . . . . factor; [eq2]
__
Solutions to [eq1] will be ...
x = 0
15x +6y = 5 . . . . . . a set of possible solutions
Solutions to [eq2] will be ...
y = 0
1 -4x = 0 ⇒ x = 1/4
Then (x, y) pairs that will satisfy both equations simultaneously are ...
(x, y) = (0, 0), (1/3, 0), (1/4, 5/24)
__
In the attached graph, solutions to [eq1] are the red lines; solutions to [eq2] are the green lines. Then simultaneous solutions to both equations are found at the intersection points of red and green lines.
If two events, A and B, never occur at the same time they are _____.
complementary
compound
simple
disjoint
Answers
Answer:
Disjoint is the correct answer.
A runner is traveling at a constant rate of 8 meters per second. How long does it take for the runner to travel 100 meters? Now before you answer this I know it's 12.5! What I need help with is creating a equation that gives the distance, d, that the person has run if you know the amount of time, t, they have been running. Thank you! :)
Answers
Answer:
see below
Step-by-step explanation:
We know that distance = rate * time
100 meters = 8 m/s * time
100 = 8t
Divide each side by 8
100/8 = 8t/8
12.5 = t
If we know the rate and the time, we can find the distance
d = rt
What is the least common denominator that will allow you to combine the constant terms? 10 21 35 or 42
Answers
Answer:
[tex]LCM = 21[/tex]
Step-by-step explanation:
Given
[tex]-\frac{3}{5}y + \frac{1}{7}= \frac{1}{3}y -\frac{2}{3}[/tex]
Required
LCM of the constant terms
Collect like terms
[tex]\frac{1}{3}y+\frac{3}{5}y = \frac{1}{7}+\frac{2}{3}[/tex]
The constant terms are on the right-hand side
To combine them, we simply take the LCM of the denominator, i.e. 7 and 3
The prime factorization of 3 and 7 are:
[tex]3 = 3[/tex]
[tex]7 = 7[/tex]
So:
[tex]LCM = 3 * 7[/tex]
[tex]LCM = 21[/tex]
The height of Mt.Whitney is approximately 14,490 feet. What is a rounded form of this number written in scientific notation?
Answers
Find the missing side. Round your answer to the nearest
Please help me
Answers
Answer:
Step-by-step explanation:
Which of the following is a geometric sequence where a1 = 4 and r = 3?
A) 4, 7, 10, 13, . . .
B) 3, 7, 11, 15, . . .
C) 4, 12, 36, 108, . . .
D) 3, 12, 48, 192, . . .
Answers
Answer:
C 4,12,36 108
Step-by-step explanation:
the answer is above.
Answer:
C
Step-by-step explanation:
G.P= a,ar,ar^2,ar^3,...,
a1=4
a2=4×3=12
a3=4×9=36
a4=4×27=108
Which is the graph of the following inequality
Answers
Answer:
graph a is the correct answer
Step-by-step explanation:
The width of a rectangle measures (7k-2m)(7k−2m) centimeters, and its length measures (5k-m)(5k−m) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answers
Answer:
[tex]P = 24k-6m[/tex]
Step-by-step explanation:
The correct expressions are:
[tex]W = 7k - 2m[/tex]
[tex]L = 5k - m[/tex]
Required
The perimeter (P)
This is calculated as:
[tex]P = 2 *(L + W)[/tex]
So, we have:
[tex]P = 2 *(5k - m + 7k -2m)[/tex]
Collect like terms
[tex]P = 2 *(5k + 7k- m -2m)[/tex]
[tex]P = 2 *(12k-3m)[/tex]
Open bracket
[tex]P = 24k-6m[/tex]
Find the mean for the data items
Answers
Answer:
4.5
Step-by-step explanation:
Given the data :
Score, x ____: 1, 2, 3, 4, 5, 6, 7, 8
Frequency, F : 1, 5, 1, 4, 4, 1, 5, 1
This is a grouped data: The mean of a grouped data is given as :
Mean (xbar) = ΣFx / ΣF
ΣFx = (1*1)+(2*5)+(3*1)+(4*4)+(5*4)+(6*1)+(7*5)+(8*1) = 99
ΣF = (1+5+1+4+4+1+5+1) = 22
Mean (xbar) = ΣFx / ΣF = 99 / 22 = 4.5
Mr. Plaggenier divided Camp Greenfield into 5 squads for an athletic scrimmages. Each squad competes against each of the other 4 squads 2 times. The scrimmage lasts 2 hours. If only one pair of teams competes at a time and all of the competitions take the same amount of time, how long is each competitions?
A)6 min.
B) 8 min.
C) 10 min.
D) 12 min.
Answers
Answer: (a)
Step-by-step explanation:
Given
There are 5 squads for an athletic scrimmages
If each team played 2 matches
Total no of matches will be
[tex]\Rightarrow \dfrac{5(5-1)}{2}\times 2=20\ \text{matches}[/tex]
So, 20 matches are played in 2 hours
Each match takes
[tex]\Rightarrow \dfrac{120}{20}=6\ \text{minute}[/tex]
Option (a) is correct.
Consider a uniform density curve defined from x = 0 to x = 8. What percent of observations fall between 1 and 5?
a) 0.20
b) 0.50
c) 0.62
d) 0.13
e) 0.63
f) None of the above
Answers
Answer: 0.50, which is choice b
Explanation:
The interval [tex]1 \le x \le 5[/tex] covers 5-1 = 4 units in the horizontal direction.
This is out of 8 units that span from x = 0 to x = 8 (we could say 8-0 = 8).
So we get the final result of 4/8 = 0.50
In other words, the interval from x = 1 to x = 5 covers exactly half of the interval from x = 0 to x = 8.
A sofa regularly sells for $760. The sale price is $676.40. Find the percent decrease of the sale price from the regular price.
Answers
Answer: (760 - 676. 40) × 100 ÷ 760 = 11%
Step-by-step explanation:
Answer:
11% decrease
Step-by-step explanation:
Concepts:
Percent change is the change between an old value and its new value represented as a %. If a percent change is a decrease, it means that the new value is less than the old value. If a percent change is a increase, it means that the old value is less than the new value. The formula for percent change is: (NV - OV)/OV · 100 = C, where NV = New Value, OV = Old Value, and C = Percent Change.The sale price is the price at which something sells or sold after the price has been reduced by sales, discounts, etc.Solving:
Let's find the percent change by using the formula.
1. Formula for Percent Change
(NV - OV)/OV · 100 = C2. Plug in the values of NV and OV
(676.40 - 760)/760 · 100 = C3. Simplify
-83.6/760 · 100 = C-0.11 · 100 = C-11 = CTherefore, our percent decrease is 11% decrease.
IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15.
(a) Find the IQ scores that represent the bottom 35%.
(b) Find the IQ score that represents the 3rd Quartile.
(c) Find the IQ score for the top 5%.
Answers
Answer:
a) IQ scores of 94.2 and below represent the bottom 35%.
b) An IQ score of 110.1 represents the 3rd quartile.
c) IQ scores of 124.7 and higher are in the top 5%.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 100 and a standard deviation of 15.
This means that [tex]\mu = 100, \sigma = 15[/tex]
(a) Find the IQ scores that represent the bottom 35%.
The 35th percentile and below, in which the 35th percentile is X when Z has a p-value of 0.35, so X when Z = -0.385.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.385 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = -0.385*15[/tex]
[tex]X = 94.2[/tex]
IQ scores of 94.2 and below represent the bottom 35%.
(b) Find the IQ score that represents the 3rd Quartile.
This is the 100*3/4 = 75th percentile, which is X when Z has a p-value of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = 0.675*15[/tex]
[tex]X = 110.1[/tex]
An IQ score of 110.1 represents the 3rd quartile.
(c) Find the IQ score for the top 5%.
IQ scores of at least the 100 - 5 = 95th percentile, which is X when Z has a p-value of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = 1.645*15[/tex]
[tex]X = 124.7[/tex]
IQ scores of 124.7 and higher are in the top 5%.
Help me again? Thanks to whomever does! Please show work!
Answers
Answer: See Below
Step-by-step explanation:
Concept:
Here, we need to know the idea of alternative interior angle, alternative exterior angle, and corresponding angles.
Alternative interior angle: a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.
Alternative exterior angle: a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.
Corresponding angle: A pair of angles that occupy the same relative position at each intersection where a straight line crosses two others.
All three kinds of angles above occur to be congruent (equal) when the lines are parallel to each other.
If you are still confused, please refer to the attachment below for a graphical explanation
Solve:
PART ONE
a) Name two pairs of alternative exterior angles: ∠1 and ∠7 / ∠2 and ∠8
b) Name two pairs of corresponding angles: ∠1 and ∠5 / ∠2 and ∠6
c) Name two pairs of alternative interior angles: ∠4 and ∠6 / ∠3 and ∠5
PART TWO
a) If the measure of angle 7 is 52°, what is the measure of angle 1?
As we can see from above, ∠1 and ∠7 are alternative exterior angles. They are part of parallel lines, thus according to the properties, they are equal.m∠1 = m∠7 = 52°b) If the measure of angle 8 is 112°, then what is the measure of angle 3?
As we can see from the figure given, ∠8 and ∠7 are linear pairs or supplementary angles, which adds up to 180°.m∠7 = 180 - m∠8 = 180 - 112 = 68°As we can see from the figure given, ∠7 and ∠3 are corresponding angles.They are part of parallel lines, thus according to the properties, they are equal.m∠3 = m∠7 = 68°Hope this helps!! :)
Please let me know if you have any questions
30 POINTS PLEASEEEEEEEEEEEE HELP
Answers
Answer:
Solution given:
f(x)=5x-3
let
y=f(x)
y=5x-3
interchanging role of x and y
x=5y-3
x+3=5y
y=[tex]\frac{x+3}{5}[/tex]
$o,
f-¹(x)=[tex]\frac{x+3}{5}[/tex]
we conclude that
f-¹(x)≠g(x)
Each pair of function are not inverses.
g(x)=x/5+3
let g(x)=y
y=x/5+3
interchanging role of x and y
x=y/5+3
x-3=y/5
doing crisscrossed multiplication
5(x-3)=y
y=5x-15
g-¹(x)=5x-15
So
g-¹(x)≠f-¹(x)
Each pair of function are not inverses.
Given that,
→ f(x) = 5x-3
Then y = f(x),
→ y = 5x-3
Now we can interchange role of x and y,
→ x = 5y-3
Then use the cross multiplication,
→ x+3 = 5y
→ y = x+3/5
Now the inverse is,
→ f-¹(x) = x+3/5
We can go to the conclusion that,
→ f-¹(x) ≠ g(x)
So, each pair of function is not inverse.
please help me its timed -H.M
Answers
Answer:
f(3) = g(3)
General Formulas and Concepts:
Algebra I
Functions
Function NotationGraphingStep-by-step explanation:
We can see from the graph that the lines intersect at (3, 6). If this is the case, then that means that when x = 3 for both functions, it outputs f(x) = 6.
Rewriting this in terms of function notation:
f(3) = 6, g(3) = 6
∴ f(3) = g(3)
Can someone help me solve this question?
Answers
Answer:
Step-by-step explanation:
I posted a pic to show you what this looks like so you have some idea of what it is I'm talking about in the explanation of how to find the side length of the rhombus. Knowing that this is a rhombus, all the sides are the same length.
Looking at the pic below, you can see that I divided the length of AC in 2 equal parts to get that the base of the right triangle I extracted below that is 8; the height is 6. We can find the side marked with a ? by using Pythagorean's Theorem; namely:
[tex]??^2=6^2+8^2[/tex] and
[tex]??^2=36+64[/tex] and
[tex]??^2=100[/tex] so
? = 10
The length of the sides of the rhombus is 10.
A jar contains 11red marbles, 12 blue marbles and 6 white marbles. Four marbles from the jar are selected. With each marble being replaced after each selection. What is the probability that the first red marble chosen is on the 5th selection?
Answers
Answer:
Red on the 5th draw = 0.0907
Step-by-step explanation:
The first to fourth selections are all the same.
Blue + white = 12 + 6 = 18
The total number of marbles is 11 + 12 + 6 = 29
P(~ red) for the first four times = (18/29)^4 = 0,1484
Now on the 5th time, the first red is 11/18
So the Probability is 0.1484 * 11/18 = 0.0907
